A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.

If 9 bags are purchased for a total cost of $36, how many three-pound bags were
purchased?

the answer is 9

Let's solve this problem step by step.

Step 1: Assign variables.
Let's assign variables to represent the unknown quantities.
Let's say:
P = number of one-pound bags purchased
T = number of three-pound bags purchased

Step 2: Set up an equation for the total cost.
The cost of one-pound bags is $2, and the cost of three-pound bags is $5. The total cost of 9 bags is $36.
So we can write the equation:
2P + 5T = 36

Step 3: Set up a second equation for the total number of bags.
The total number of bags purchased is 9.
So we can write the equation:
P + T = 9

Step 4: Solve the system of equations.
We have two equations with two variables. We can solve this system of equations using substitution or elimination.

Let's use the substitution method:
From equation 3, we can isolate P as follows:
P= 9 - T

Substitute this value for P in equation 2:
2(9 - T) + 5T = 36

Simplify the equation:
18 - 2T + 5T = 36
3T = 36 - 18
3T = 18
T = 18 / 3
T = 6

Step 5: Find the value of P.
Now substitute the value of T into equation 3:
P = 9 - T
P = 9 - 6
P = 3

Step 6: Answer the question.
According to the solution, 3 three-pound bags were purchased.

Therefore, 3 three-pound bags were purchased.

To solve this problem, let's assign variables to the unknown quantities. Let's say the number of one-pound bags purchased is represented by x, and the number of three-pound bags purchased is represented by y.

Given that one-pound bags cost $2 and three-pound bags cost $5, we can create equations based on the given information.

First, we know that the total cost of all the bags purchased is $36. This can be expressed as:
2x + 5y = 36

We also know that the total number of bags purchased is 9. This can be expressed as:
x + y = 9

To solve these equations, we can use a method called substitution. We can solve one equation for one variable and then substitute that value into the other equation.

Let's solve the second equation for x:
x = 9 - y

Now, we can substitute this value of x into the first equation:
2(9 - y) + 5y = 36
18 - 2y + 5y = 36
3y = 36 - 18
3y = 18
y = 6

Therefore, 6 three-pound bags were purchased.

O + T = 9

T = 9 - O

2O + 5T = 36

Substitute 9-O for T in last equation and solve for O. Insert that value into the first equation and solve for T. Check by inserting both values into the second equation.